Flexible and conformal electronics using rigid substrates

ABSTRACT

A flexible electronics assembly includes a single-piece substrate having two regions of rigidity separated by a localized region of flexibility. The localized region of flexibility has a lower rigidity than the two regions of rigidity. The two regions of rigidity are angularly deflectable from a planar configuration of the single-piece substrate to a non-planar configuration of the single-piece substrate by hinging action of the localized region of flexibility. At least one electronic component is mounted on at least one of the two regions of rigidity.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional of, and claims priority to U.S. patentapplication Ser. No. 15/650,453 filed on Jul. 14, 2017, which is anon-provisional of, and claims to priority to, U.S. ProvisionalApplication No. 62/362,314, entitled: “Flexible and conformalelectronics using rigid substrates,” filed on Jul. 14, 2016, thedisclosures of which are hereby incorporated by reference in theirentireties.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under NSF Grant No.EFRI-ODISSEI-1240417 funded by the National Science Foundation. Thegovernment has certain rights in the invention.

TECHNICAL FIELD

This disclosure relates to the use of compliant mechanisms in flexibleelectronics.

BACKGROUND

In traditional electronics, electronic components (e.g., integratedcircuits, solar cells, etc.) are mounted on rigid printed circuit boards(PCBs) for mechanical support and ease of manufacturing. The PCBs, whichmay be copper clad, may be made of high strength glass-reinforced epoxylaminates with physical and chemical properties that conform to industrystandard grades (e.g., G10, G11, FR4, FR5 and FR6) regulated by theNational Electrical Manufacturers Association (NEMA). Rigid PCBs may notbe desirable in many applications.

SUMMARY

In a general aspect, a flexible electronics assembly is made tom asingle-piece substrate. The substrate includes two regions of rigidityseparated by a localized region of flexibility having a lower rigiditythan the two regions of rigidity. At least one electronic component ismounted on at least one of the two regions of rigidity. The two regionsof rigidity are angularly deflectable from a planar configuration of thesingle-piece substrate to a non-planar configuration of the single-piecesubstrate by hinging action of the localized region of flexibility. Thelocalized region of flexibility elastically accommodates substantiallyall stresses and strains in the single-piece substrate caused by angulardeflection of the two regions of rigidity.

In an aspect, the localized region of flexibility is a geometricallymodified region of the single-piece substrate, which includes at leastone compliant joint (e.g., a lamina emergent torsional (LET) joint)formed by geometrical shaping of the single-piece substrate. Thecompliant joint is configured to transfer a bending load associated withangular deflection of the two regions of rigidity and applied to thecompliant joint as a torsional load on torsional members of thecompliant joint.

In a further aspect, the single-piece substrate is a printed circuitboard (PCB) (e.g., a conductor clad epoxy-glass laminate). Anelectrically conducting trace running across the localized region offlexibility provides an electrical connection to the at least oneelectronic component mounted on at least one of the two regions ofrigidity.

In a general aspect, a method includes geometrically modifying asingle-piece substrate to include a localized region of flexibilityseparating two regions of rigidity. The localized region of flexibilityhas a lower rigidity than the two adjoining regions of rigidity. Themethod includes configuring the localized region of flexibilityseparating the two regions of rigidity as a hinge to angularly deflectthe two regions of rigidity from a planar configuration of thesingle-piece substrate to a non-planar configuration of the single-piecesubstrate.

In an aspect, geometrically modifying a single-piece substrate toinclude a localized region of flexibility includes configuring thelocalized region of flexibility to elastically accommodate substantiallyall stresses and strains in the single-piece substrate caused by angulardeflection of the two regions of rigidity, for example, by forming atleast one compliant joint by geometrical shaping of the single-piecesubstrate. The geometrical shaping of the single-piece substrateincludes forming a lamina emergent torsional (LET) joint.

In an aspect, forming at least one compliant joint by geometricalshaping of the single-piece substrate includes forming a lamina emergenttorsional (LET) joint or an array of such joints. An example LET jointcan include two torsional members and two bending members as sides of arectangle circumscribing a rectangular slot cut in the localized regionof flexibility.

In an aspect, the single-piece substrate is a conductor clad printedcircuit board (PCB) with physical and chemical properties that conformto industry standard grades regulated by the National ElectricalManufacturers Association (NEMA), and geometrically modifying thesingle-piece substrate to include a localized region of flexibilityincludes forming an electrically conducting trace running across thelocalized region of flexibility.

In a further aspect, geometrically modifying the single-piece substrateto include a localized region of flexibility includes forming aplurality of localized regions of flexibility along fold axes of anorigami pattern (e.g., a map fold origami pattern).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view illustration of an example electronicsassembly made in an initial planar configuration on a monolithicsubstrate having a localized region of flexibility, in accordance withthe principles of the present disclosure.

FIG. 2 is a cross-sectional view of the example electronics assembly ofFIG. 1 with regions of high rigidity moved from the initial planarconfiguration to a relative non-planar configuration by hinging actionof the localized flexible region, in accordance with the principles ofthe present disclosure.

FIG. 3A is an illustration of an example lamina emergent torsional (LET)joint, in accordance with the principles of the present disclosure.

FIG. 3B is an illustration of a prototype array of LET joints, inaccordance with the principles of the present disclosure.

FIG. 4A is an illustration of an LET joint being represented by acorresponding spring system for an analytical model, in accordance withthe principles of the present disclosure.

FIG. 4B is a drawing illustration of the dimensional parameters of a LETjoint used in an analytical model of the LET joint, in accordance withthe principles of the present disclosure.

FIG. 5 is a schematic illustration of the moment on a LET jointresulting from an applied angular deflection.

FIG. 6A is a schematic illustration of an example array of LET joints.

FIG. 6B is a table comparing results of an analytical model expressionand finite element analysis for the Von Mises stress of an array of LETjoints.

FIG. 7A is an illustration of an as-fabricated planar configuration ofsolar panels mounted on rigid portions of a copper-clad PCB substrate,in accordance with the principles of the present disclosure.

FIG. 7B is an illustration of an LET joint array used in the prototypefolding solar panel assembly of FIG. 7A, in accordance with theprinciples of the present disclosure.

FIG. 7C is an illustration of the prototype folding solar panel assemblyof FIG. 7A in a folded configuration, in accordance with the principlesof the present disclosure.

FIG. 8 is a table listing results of resistance measurements on theelectrical connectivity of structures similar to those used in theprototype folding solar panel assembly of FIG. 7A.

FIG. 9A is an illustration of an origami pattern used for a foldablePCB-based structure, in accordance with the principles of the presentdisclosure.

FIG. 9B is an illustration of fold regions in the origami pattern ofFIG. 9A that can be made flexible with surrogate hinges for making afoldable PCB-based structure, in accordance with the principles of thepresent disclosure.

FIG. 9C is an illustration of regions of optimized surrogate foldgeometry in the origami pattern of FIG. 9A for making a foldablePCB-based structure, in accordance with the principles of the presentdisclosure.

FIG. 10 is an illustration of an example origami-like folding structurefor the origami that can be designed with optimized surrogate hinge LETjoint arrays, and fabricated from a single sheet of copper-clad FR-4 PCBmaterial, in accordance with the principles of the present disclosure.

FIG. 11 is an illustration of an example method for making PCBsubstrate-based flexible electronics, in accordance with the principlesof the present disclosure.

DETAILED DESCRIPTION

Flexible electronics are used in a wide array of industries (e.g.,aerospace, automotive, consumer electronics, and medical deviceindustries) in applications where it is necessary confine electronicsinto small spaces or to conform the electronics to arbitrary shapes.

Flexible electronics are typically composed of a bilayer of thinpassive, but flexible, substrate (e.g., plastic, textile, etc.) toppedwith a second layer of active electronic components. Flexible circuitsare often used as connectors in various applications where flexibility,space savings, or production constraints limit the serviceability ofrigid circuit boards or hand wiring.

The stiffness and rigidity of the traditional rigid PCBs limits use inapplications that require high flexibility (i.e., flexible electronics).Modification of PCBs for use in flexible electronics can requirethinning of the substrate material to reduce substrate stiffness andincrease flexibility, but at the cost of reduced mechanical strength.However, the reduced substrate stiffness v. mechanical strengthtrade-offs can cause undesirable behavior in some parts of theelectronics. In particular, fatigue due to repeated mechanicaldeflection of components mounted on thinned PCBs and their electricalconnectors can lead to electrical or mechanical degradation or failure.

Electronics assemblies built on compliant mechanisms, and methods formaking the same are described herein.

A compliant mechanism may be an otherwise rigid monolithic (i.e.,single-piece, all formed of the same material or from a single piece ofmaterial) substrate (e.g., a printed circuit board (PCB) substrate) thatis geometrically shaped or modified to include at least a localizedregion of low stiffness, in accordance with the principles of thepresent disclosure. The localized region of low stiffness (e.g., lowerstiffness than adjacent or other regions), which can act as a flexiblehinge or fold, is obtained by modification of local geometric featuresof the localized region. In contrast, traditional methods for obtaininglow stiffness substrates (e.g., by material selection) may involvereducing the stiffness of the PCB substrate globally.

In some implementations, multiple localized regions can be included in aPCB. The multiple localized regions may be aligned along differentdirections (e.g., non-parallel, perpendicular) and/or may be included ina portion (rather across the entirety of) a PCB.

A localized region of low stiffness of the compliant mechanismsdisclosed herein may include one or more compliant joints.

The terms rigidity and stiffness, which may be used interchangeablyherein, are terms describing elastic properties of a material or object.The term flexible, can also refer to elastic properties of a material orobject, and may be understood to be the converse of rigid. Further, thelocalized region of low stiffness may be referred to as the flexibleregion or the surrogate hinge.

While example embodiments described herein may include variousmodifications and alternative forms, embodiments thereof are shown byway of example in the drawings and will be described herein. It shouldbe understood, however, that there is no intent to limit exampleembodiments to the particular forms disclosed, but on the contrary,example embodiments are to cover all modifications, equivalents, andalternatives falling within the scope of the claims. Furthermore, thefigures are intended to illustrate the general characteristics ofmethods and/or structure utilized in certain example embodiments and tosupplement the written description provided below. These figures arenot, however, to scale and may not precisely reflect the precisestructural or performance characteristics of any given embodiment, andshould not be interpreted as defining or limiting the range of values orproperties encompassed by example embodiments. For example, thestructural elements may be reduced or exaggerated for clarity. The useof similar or identical reference numbers in the various drawings isintended to indicate the presence of a similar or identical element orfeature.

An example electronics assembly may include a layer of one or moreelectronic or electrical devices (which can be referred to as electroniccomponents), a patterned layer of a conductor material that electricallyinterconnects the one or more electronic components, and a supportingmonolithic (i.e., single-piece) substrate. The monolithic substrate maybe an otherwise rigid circuit board with two regions of rigidity (e.g.,high rigidity) separated by a localized region of flexibility (e.g., lowrigidity), in accordance with the principles of the present disclosure.The localized region of flexibility may have a rigidity that is lowerthan the rigidity of the two regions of rigidity. The localized regionof flexibility may act as a surrogate hinge or joint that can be used toangularly deflect the two regions of rigidity of the monolithicsubstrate to a non-planar configuration without bending the two regionsof rigidity or introducing stress or strain in the deflected regions ofrigidity. Electronic components mounted on either of the two regions ofrigidity may not suffer any additional stress or strain when the tworegions of rigidity are deflected to the non-planar configuration fromthe initial planar configuration by hinging or bending action of thelocalized region of flexibility.

FIG. 1 is a cross-sectional view of an example electronics assembly 100made in an initial planar configuration on a monolithic substrate havinga localized region of flexibility, in accordance with the principles ofthe present disclosure.

Electronics assembly 100 may include a conductor layer 10 a disposed ona monolithic substrate 10 b. Conductor layer 10 a may be obtained orincluded on substrate 10 b as part of a printed circuit board (PCB) 10(e.g., a single sheet of copper-clad FR-4 material). PCB 10 may includea localized region (e.g., flexible region 10 d) of low rigidity orstiffness interposed between two regions of high rigidity (e.g., rigidpanel 10 c and rigid panel 10 e).

In electronics assembly 100, electronic components (e.g., electroniccomponent 11 a and electronic component 11 b) may be mounted (e.g., bysoldering techniques) on the regions of high rigidity (e.g., rigid panel10 c and rigid panel 10 e, respectively).

In example implementations, flexible region 10 d may include one or morecompliant joints (e.g., lamina emergent torsional (LET) joint 300, FIG.3A). The compliant joints may be formed, for example, by geometricalshaping (e.g., by cutting, milling, etching, etc.) of PCB 10.

FIG. 2 is a cross-sectional view of example electronics assembly 100with the regions of high rigidity (e.g., rigid panel 10 c and rigidpanel 10 e, respectively) moved or angularly deflected from the initialplanar configuration shown in FIG. 1 to a relative non-planarconfiguration by hinging action of flexible region 10 d, in accordancewith the principles of the present disclosure. It may be noted thatmechanical strains or stresses created in moving electronics assembly100 to the relative non-planar configuration shown in FIG. 2 may beelastically accommodated in flexible region 10 d by design of thegeometric structure and parameters of flexible region 10 d, inaccordance with the principles of the present disclosure.

FIG. 3A shows, for example, the geometry of an example LET joint 300that may be formed in flexible region 10 d of PCB 10, in accordance withthe principles of the present disclosure. LET joint 300 (as shown inFIG. 3A) has, for example, a rectangular slot geometry. LET joint 300may, for example, include torsional members 310 and bending member 320as sides of a rectangle circumscribing a rectangular slot 330 cut inflexible region 10 d of PCB 10. The geometry of LET joint 300 may bedesigned so that a bending load (applied around axis 340) is transferredas a torsional load on torsional members 310 to lower the stiffness offlexible region 10 d.

Further, flexible region 10 d may be geometrically shaped to includemultiple LET joints 300 that are disposed in an array (e.g., as a seriesand or a parallel pattern of joints) designed to reduce the stiffness offlexible region 10 d to a target level. The multiple LET joints 300 maymake flexible region 10 d act as a flexible surrogate hinge or fold inPCB 10. The multiple LET joints 300 may serve a mechanical purpose oflowering the stiffness of flexible region 10 d and also serve as anelectrical connector between rigid panel 10 c and rigid panel 10 e byvirtue of electrically conducting traces that may be formed by residualconductor layer 10 b coupled to (e.g., deposited on) top of the multipleLET joints 300. The electrically conducting traces may be formed whenflexible region 10 d of PCB 10 is geometrically shaped (e.g., bycutting, milling, or etching) to form the multiple LET joints 300.

FIG. 3B shows, for example, a prototype array 350 of LET joints 300 thatmay be formed in flexible region 10 d of PCB 10, in accordance with theprinciples of the present disclosure. Array 350 may act as a surrogatehinge or fold allowing relative hinge-like motion of rigid panel 10 cand rigid panel 10 e (as shown, for example, in FIG. 2). Electricallyconducting traces 340 formed in conductor layer 10 b may run across LETjoints 300 in array 350 to electrically connect electronic components(e.g., electrical components 11 a and electrical component 11 b shown inFIGS. 1 and 2) that may be disposed, for example, on rigid panel 10 cand rigid panel 10 e. Thus, array 350 formed in flexible region 10 d ofPCB 10 in addition to serving as a mechanical hinge can also serve as anelectrical connector between rigid panel 10 c and rigid panel 10 e.

While a LET joint (e.g. LET joint 300) with a rectangular slot geometryhas been used in the foregoing for purposes of illustration as anexample type of surrogate hinge or fold that may be fabricated bygeometric shaping of flexible region 10 d of PCB 10, other additional oralternate types of surrogate hinges or folds may be used to make acompliant member with a hinge-like motion capability. The otheradditional or alternate types of surrogate hinges or folds may, forexample, include inverted lamina emergent joints (I-LEJ), tension laminaemergent joints (T-LEJ), blending-orthogonal joints, inverted blendingorthogonal joints, mixed tension resistant, mixed compression resistantjoints, and/or torsion-parallel joints, etc.

Flexibility of flexible region 10 d of PCB 10 may be controlled bymodifying geometric parameters such as the number of arrayed LET jointsand the dimensional parameters of the LETs (e.g., torsion member length,torsion member width, bending member length, bending member width,thickness t, etc.).

In example implementations, the type and the geometric dimensions ofsurrogate hinges or folds used in flexible region 10 d may be determinedfor an electronic assembly application by analytical and/or finiteelement analysis ((FEA) modelling.

Analytical Model

An analytical model for analyzing a single LET joint (e.g., LET joint300) and arrays of LET joints is described in more detail below. In theanalytical model, single LET joint 300 is represented by a springsystem. FIG. 4A shows, for example, LET joint 300 being represented by acorresponding spring system 300S. In spring system 300S, torsionalmembers 310 of LET joint 300 are represented by springs with springconstants k₁-k₄ and bending members 320 are represented by springs withspring constants k₅ and k₆. Further, FIG. 4B shows, for reference, thedimensional parameters (e.g., torsion member length l_(t), torsionmember width w_(t), bending member length l_(b), bending member widthw_(b), and thickness t, etc.) of LET joint 300 that are used in theanalytical model.

The analytical model can assume, in some implementations, that a puremoment is applied to LET joint 300, and moment-deflection behavior ofLET joint 300 is characterized by the equation.M=k _(eq)*θ  (1)

where as shown in FIG. 5, M is the moment on the joint resulting from anapplied angular deflection θ, and k_(eq) is an equivalent springconstant based on a combination of spring constants k₁-k₆ of springsystem 300S.

Combining the springs of spring system 300S results in an equivalentspring constant of

$\begin{matrix}{k_{eq} = {\frac{k_{1}k_{3}k_{5}}{{k_{1}k_{3}} + {k_{1}k_{5}} + {k_{3}k_{5}}} + \frac{k_{2}k_{4}k_{6}}{{k_{2}k_{4}} + {k_{2}k_{6}} + {k_{4}k_{6}}}}} & (2)\end{matrix}$

Assuming that a symmetric LET joint is used, k₁=k₂=k₃=k₄ and k₅=k₆ forthe torsional members of the LET joint. Since k₁-k₄ are the stiffnessesof the symmetric torsional members, they may be represented as k_(t).Likewise, k₅ and k₆ are the stiffnesses of the symmetric bending membersand may be represented as k_(b). Combining the above stiffnesses assprings in parallel and series (e.g. as shown in spring system 300S)yields the equivalent stiffness of a single LET joint in terms of thestiffness of its torsional and bending members as:

$\begin{matrix}{k_{eq} = \frac{2k_{t}k_{b}}{k_{t} + {2k_{b}}}} & (3)\end{matrix}$

To find the total equivalent stiffness, the stiffnesses of the torsionaland bending members is calculated. The torsional stiffness k_(t) iscalculated by

$\begin{matrix}{k_{t} = \frac{K_{i}G}{l_{t}}} & (4)\end{matrix}$

where G is the modulus of rigidity, l_(t) is the length of the torsionalmember, and K_(i) is a geometry-dependent parameter defined by

$\begin{matrix}{K_{i} = {w_{t}{t^{3}\left\lbrack {\frac{1}{3} - {0.21\frac{t}{w_{t}}\left( {1 - \frac{t^{4}}{12w_{t}^{4}}} \right)}} \right\rbrack}}} & (5)\end{matrix}$where t is the thickness of the LET joint and w_(t) is the width of thetorsional member.

The bending stiffness k_(b) is calculated by

$\begin{matrix}{k_{b} = \frac{{Ew}_{b}t^{3}}{12l_{b}}} & (6)\end{matrix}$

where E is the modulus of elasticity, w_(b) is the width of the bendingmember, and l_(b) is the length of the bending member.

The shear stress in a non-circular torsion member can be modeled by theequation

$\begin{matrix}{\tau_{\max} = \frac{T_{i}}{Q}} & (7)\end{matrix}$

where T_(i) is the torque applied to the torsional member and Q is ageometry-dependent parameter, defined for a rectangular cross section asfollows:

$\begin{matrix}{Q = \frac{w_{t}^{2}t^{2}}{{3w_{t}} + {1.8t}}} & (8)\end{matrix}$

The bending stress in the bending members can be calculated by

$\begin{matrix}{\sigma_{\max} = \frac{6T_{i}}{w_{b}t^{2}}} & (9)\end{matrix}$

where T_(i) is the torque applied to the bending member, w_(b) is thewidth of the bending member, and t is the thickness of the bendingmember.

It is important to note that T_(i) for both shear and bending isequivalent to half of the moment applied to the joint, since there aretwo torsion and two bending members in parallel and the load is shared.Therefore, T_(i) is given as

$\begin{matrix}{T_{i} = \frac{M}{2}} & (10)\end{matrix}$

for a single LET joint.

The maximum Von Mises stress, σ_(max,v), can then be calculated fromτ_(max) and σ_(max) asσ_(max,v)=√{square root over (σ_(max) ²+3τ_(max) ²)}  (11)

Combining equations 1 through 11, it is possible to determine themaximum stress in the joint with respect to the applied angulardeflection θ as

$\begin{matrix}{\sigma_{\max,v} = {\frac{K_{i}G}{l_{i}}\theta\sqrt{\frac{9}{w_{b}^{2}t^{4}} + \frac{3}{4Q^{2}}}}} & (12)\end{matrix}$

in cases where m joints are arrayed in parallel, the torque on eachjoint is equal to the applied torque divided by m. In cases where njoints are arrayed in series, the angular deflection on each joint isequal to the total angular deflection divided by n. FIG. 6A shows, forexample, an example array 600 which includes m==2 LET joints in paralleland n=5 LET joints in series. The maximum Von Mises stress of a LETjoint array with in joints in parallel and n joints in series is thengiven by

$\begin{matrix}{\sigma_{\max,v} = {\frac{2k_{t}k_{b}\theta}{n\left( {k_{t} + {2k_{b}}} \right)}\sqrt{\frac{9}{w_{b}^{2}t^{4}} + \frac{3}{4Q^{2}}}}} & (13)\end{matrix}$

Substituting equation 4 and 6 into equation 13 yields the followinganalytical model expression for the maximum Von Mises stress, σ_(max,v)for an array of LET joints:

$\begin{matrix}{\sigma_{\max,v} = {\frac{2\left( \frac{K_{i}G}{l_{t}} \right)\left( \frac{{Ew}_{b}t^{3}}{12l_{b}} \right)}{\left( \frac{K_{i}G}{l_{t}} \right) + {2\left( \frac{{Ew}_{b}t^{3}}{12l_{b}} \right)}}\sqrt{\frac{9}{w_{b}^{2}t^{4}} + \frac{3}{4Q^{2}}}}} & (14)\end{matrix}$

The above analytical model expression can be verified using finiteelement analysis (FEA) described below.

Finite Element Analysis (FEA) Model

A finite element analysis can verify the analytical model expression(i.e., equation 14) for the maximum Von Mises stress, σ_(max,v), for anarray of LET joints. Various m×n arrays of LET joints (with m being thenumber of LET joints in parallel and n being the number of LET joints inseries) can be modeled and then loaded to an angular deflection θ=180°.Various design languages (e.g., ANSYS Parametric Design Language) can beused to perform the analysis. In some implementations, for example,Solid186 elements can be used to model the torsional members, andBeam188 elements can be used to model the rigid regions (e.g., rigidpanel 10 c and rigid panel 10 e) at the ends of the design. The modelcan be meshed into about 188 elements per torsional member. Because ofthe large deflection of the structure, a nonlinear solver can be used.

The FEA model results for the maximum Von Mises stress can be comparedto the analytical model expression (equation 14, above) for the maximumVon Mises stress. Results of an example comparison of the analytical andfinite element model results are listed in Table 1 in FIG. 6B. In Table1, the Von Mises stress is listed based on a 180° angular displacement,and m is the number of LET joints in parallel and n is the number of LETjoints in series (see FIG. 5). Further in Table 1, the differencesbetween the results of the two models are expressed as a percentage ofthe total Von Mises stress. It may be noted that in all (or nearly all)cases, the differences are within 8%. Sources of error may include theassumptions that LET members can be loaded in pure tension and bendingin the FEA model, and that all other components can be rigid.

Prototype Flexible Electronics Assembly

The analytical model and finite element analysis (FEA) model fordetermining the maximum Von Mises stress for an array of LET jointsdescribed above may facilitate the design of flexible electronicsassemblies that use otherwise rigid substrates (e.g., traditional PCBsubstrates) to support electronic components. In assignee's facilities,one such design for a folding solar panel assembly can be prototyped andtested to investigate the feasibility of using an array of LET joints asa means of introducing flexibility in rigid PCB-based electronics.

FIGS. 7A, 7B and 7C show aspects of a folding solar panel assembly 700.Folding solar panel assembly 700 can be designed to fold 180° about asurrogate hinge, and stow in, for example, a backpack.

FIG. 7A shows an as-fabricated folding solar panel assembly 700 in aplanar configuration with solar panel 701 and solar panel 702 mounted onrigid portions (e.g., like rigid panel 10 c and rigid panel 10 e) of acopper-clad PCB substrate (e.g., PCB substrate 704, FIG. 7C). The rigidportions of the PCB substrate are separated by a region of flexibility(e.g., like flexible region 10 d) created by fabricating an array of LETjoints 703 (similar to array 600) in the PCB substrate. Copper conductortraces (e.g. traces 705, FIG. 7B) across the array of LET joints 703provided electrical connection between solar panel 701 and solar panel702.

As designed, array of joints 703 included 2 LET joints in parallel and 5LET joints in series (m=2, n=5). The torsional members of each LET jointhad a length of l_(t)=3.68 and a width of w_(t)=0.13 cm. The bendingmembers of each LET joint had a length of l_(b)=0.38 cm and a width ofw_(b)=0.13 cm. Overall, the hinge section (i.e. array of joints 703) canbe 15.24 cm along the bending axis and 2.16 cm perpendicular to thebending axis.

FIG. 7B provides a detail view of LET joint array 703 with exposedcopper traces 705.

FIG. 7C shows a view of folding solar panel assembly 700 in a non-planarconfiguration in which solar panel 701 has been deflected by 180 degreesto be disposed on (e.g., lie on top of) solar panel 702 by hingingaction of array of LET joints 703 in PCB substrate 704.

Folding solar panel assembly 700, as fabricated, demonstrates theability to deflect 180° without mechanical failure or degradation ofelectrical performance.

To simulate repeated use of folding solar panel assembly 700, a fatiguetesting device can be customized to accommodate the hinge portion (e.g.array of LET joints 703) of a PCB substrate (e.g., PCB substrate 704)used for folding solar panel assembly 700. Two copies of the hingeportion can be produced and tested. On each hinge portion, twoelectrically conducting traces can be routed through the LET joints onthe top, and two electrically conducting traces can be routed throughthe LET joints on the bottom. A microcontroller (e.g., an Arduino Unowith ATmega328P) can be connected to each LET joint with a resistor inseries and used as a voltage source and measurement device. The fatiguetesting device can be used to repeatedly deflect rigid portions of thePCB substrate 180° at a rate of 20 cycles per minute. Voltage samplescan be taken at a rate of 140 samples per minute to detect ifconductivity of the electrically conducting traces routed through theLET joints can be interrupted or broken.

The samples can be deflected for 100,000 cycles. After the test, thesamples can be inspected for mechanical failure. The resistance of eachelectrically conducting trace across the hinge can be also measuredbefore and after testing. Results of the resistance measurements arelisted in Table 2 in FIG. 8. In Table 2, resistance measurements on twoboards before and after 1000,000 cycles of deflection are listed for ofeach trace (e.g., traces A, B, C and D). All resistance values shown arein ohms (Ω).

As shown in Table 2, the average resistance change of the electricallyconducting traces after 100,000 cycles can be only 1.9%. As no crackingor other mechanical failure of the electrically conducting traces can beobserved, this small 1.9% increase in resistance is likely due toincreased contact resistance from dust particles settling on the surfacein the test environment.

Origami Folding Structures

To further demonstrate how the foregoing techniques for introducingflexible regions (i.e., arrays of LET joints) in a rigid substrate toform surrogate hinges allow manufacture of stowable PCB-based flexibleelectronic assemblies, a prototype origami-like structure can bedesigned and fabricated from a single sheet of epoxy-fiberglass laminatePCB (e.g., a copper-clad FR-4 fiberglass PCB).

FIG. 9A shows an origami pattern (e.g., map fold origami pattern 900)with two degree-four vertices that can be selected for the demonstrativeprototype origami-like structure (e.g., fabricated structure 1000, FIG.10). In FIG. 9A, labels A, B, and C indicate an order of folds forfolding the single sheet PCB. The single sheet PCB is first folded inhalf on fold A and then folded in thirds on folds B and C.

FIG. 9B shows regions 910 where flexibility can be added to a singlesheet PCB to facilitate folding. FIG. 9C shows three surrogate hingeregions (labelled as α, β, and γ) that can be included in the singlesheet PCB. Regions shown in a cross hatched pattern can be cut out. Whenthe single sheet PCB is folded, the α regions are folded first, so the αregions can have (e.g., can be optimized to have) a small bend radiuswhen folded. The β and γ regions are folded next, with γ0 regions foldedaround β regions. Therefore, the β regions can have (e.g., can beoptimized to have) a small bend radius, and γ regions can have (e.g.,can be optimized to have) a have a larger bend radius than the β regionsto fold around the outside of the B folds.

For optimizing the geometry of surrogate hinge structures for the threesurrogate hinge regions α, β, and γ, an optimization routine can be usedfor an array of LET joints with m members in parallel and n members inseries. Mixed integer programming can be implemented using, for example,various algorithms (e.g., APMonitor modeling language and IPOPT solver).The structures for the three surrogate hinge regions α, β, and γ can beeach solved separately. Inside fold regions α and β can (e.g., can beoptimized to) reduce or minimize an objective function based on width ofthe fold while satisfying maximum Von Mises stress constraints. Outsidefold region γ can (e.g., can be optimized to) reduce or minimize VonMises stress while satisfying geometric constraints which would allowthe g folds to be folded around the b folds.

The dimensions (e.g., optimized dimensions) for the surrogate hinge canbe w_(t)=0.10 cm, l_(t)=1.57 cm, w_(b)=0.10 cm, and l_(b)=0.10 cm, withm=2 members in parallel and n=6 members in series. The dimensions (e.g.,optimized dimensions) for the β hinge can be w_(t)=0.10 cm, l_(t)=1.93cm, w_(b)=0.10 cm, and l_(b)=0.10 cm, with m=2 members in parallel andn=5 members in series. The dimensions (e.g., optimized dimensions) forthe γ hinge can be w_(t)=0.10 cm, l_(t)=1.83 cm, w_(b)=0.10 cm, andl_(b)=0.10 cm, with m=2 members in parallel and n=15 members in series.The thickness (e.g., optimized thickness) of the structure can be 0.079cm.

The entire prototype origami-like structure (e.g., fabricated structure1000, FIG. 10) can be fabricated from a single sheet of PBC using, forexample, a computer numerical control (CNC) mill to shape arrays of LETjoints for the three surrogate hinge regions α, β, and γ in the singlesheet of PBC.

FIG. 10 shows an example of the fabricated structure 1000 being foldedsequentially. In its folded state, fabricated structure 1000 occupiesapproximately 17% of its original footprint.

FIG. 11 shows an example method 1100 for making PCB substrate-basedflexible electronics, in accordance with the principles of the presentdisclosure.

In an example implementation, method 1100 includes geometricallymodifying a single-piece substrate to include a localized region offlexibility separating two regions of rigidity (1110). The localizedregion of flexibility has a lower rigidity than the two regions ofrigidity. Method 1100 further includes using the localized region offlexibility separating the two regions of rigidity as a hinge in thesingle-piece substrate to angularly deflect the two regions of rigidityfrom a planar configuration of the single-piece substrate to anon-planar configuration of the single-piece substrate (1120).

In method 1100, geometrically modifying a single-piece substrate toinclude a localized region of flexibility 1110 includes configuring thelocalized region of flexibility to elastically accommodate substantiallyall stresses and strains in the single-piece substrate caused by angulardeflection of the two regions of rigidity.

Further, geometrically modifying a single-piece substrate to include alocalized region of flexibility 1110 includes forming at least onecompliant joint by geometrical shaping of the single-piece substrate.Forming the at least one compliant joint by geometrical shaping of thesingle-piece substrate may include forming a lamina emergent torsional(LET) joint. Forming at least one compliant joint by geometrical shapingof the single-piece substrate may include forming an array of LETjoints.

In method 1100, forming the LET joint includes forming two torsionalmembers and two bending members as sides of a rectangle circumscribing arectangular slot cut in the localized region of flexibility, andconfiguring the LET joint to transfer a bending load associated withangular deflection of the two regions of rigidity and applied to the LETjoint as a torsional load on the two torsional members of the LET joint.

In method 1100, the single-piece substrate may be a conductor cladprinted circuit board (PCB) (e.g., a single sheet of copper-clad FR-4fiberglass) with physical and chemical properties that conform toindustry standard grades regulated by the National ElectricalManufacturers Association (NEMA), and geometrically modifying thesingle-piece substrate to include a localized region of flexibility 1110may include forming an electrically conducting trace running across thelocalized region of flexibility.

Method 1100 may include utilizing the electrically conducting tracerunning across the localized region of flexibility to provide anelectrical connection to at least one electronic component mounted thatmay be mounted on at least one of the two regions of rigidity.

In some example implementations wherein geometrically modifying thesingle-piece substrate to include a localized region of flexibility 1110includes forming a plurality of localized regions of flexibility alongfold axes of a map fold origami pattern.

The techniques describe herein may be used to conform PCBs to anarbitrary shape (e.g., for flexible electronics applications). Forexample, PCBs could be folded for installation in confined spaces. PCBscould be designed with multiple panels that could fit within a limitedspace or against the walls of a container. PCBs could be folded to savespace in stowing and deployed for increased surface area during use.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the embodiments.As used herein, the singular forms “a,” “an,” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises,”“comprising,” “includes,” and/or “including,” when used in thisspecification, specify the presence of the stated features, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, steps, operations,elements, components, and/or groups thereof.

It will be understood that when an element is referred to as being“coupled,” “connected,” or “responsive” to, or “on,” another element, itcan be directly coupled, connected, or responsive to, or on, the otherelement, or intervening elements may also be present. In contrast, whenan element is referred to as being “directly coupled,” “directlyconnected,” or “directly responsive” to, or “directly on,” anotherelement, there are no intervening elements present. As used herein theterm “and/or” includes any and all combinations of one or more of theassociated listed items.

Spatially relative terms, such as “beneath,” “below,” “lower,” “above,”“upper,” and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, the term “below” can encompass both an orientation ofabove and below. The device may be otherwise oriented (rotated 90degrees or at other orientations) and the spatially relative descriptorsused herein may be interpreted accordingly.

Example embodiments of the flexible circuit boards are described hereinwith reference to cross-sectional illustrations that are schematicillustrations of idealized embodiments (and intermediate structures) ofexample embodiments. As such, variations from the shapes of theillustrations as a result, for example, of manufacturing techniquesand/or tolerances, are to be expected. Thus, example embodiments of thepresent inventive concepts should not be construed as limited to theparticular shapes of regions illustrated herein but are to includedeviations in shapes that result, for example, from manufacturing.Accordingly, the regions illustrated in the figures are schematic innature and their shapes are not intended to illustrate the actual shapeof a region of a device and are not intended to limit the scope ofexample embodiments.

It will be understood that although the terms “first,” “second,” etc.may be used herein to describe various elements, these elements shouldnot be limited by these terms. These terms are only used to distinguishone element from another. Thus, a “first” element could be termed a“second” element without departing from the teachings of the presentembodiments.

While certain features of the described implementations have beenillustrated as described herein, many modifications, substitutions,changes, and equivalents will now occur to those skilled in the art. Itis, therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the scope of theimplementations. It should be understood that they have been presentedby way of example only, not limitation, and various changes in form anddetails may be made. Any portion of the apparatus and/or methodsdescribed herein may be combined in any combination, except mutuallyexclusive combinations. The implementations described herein can includevarious combinations and/or sub-combinations of the functions,components, and/or features of the different implementations described.

What is claimed is:
 1. A method, comprising: geometrically modifying asingle-piece substrate to include two regions of rigidity separated by alocalized region of flexibility, the localized region of flexibilityhaving a lower rigidity than the two regions of rigidity, the localizedregion of flexibility including a plurality of compliant joints, theplurality of compliant joints including at least one lamina emergenttorsional (LET) joint; and configuring the plurality of compliant jointsincluding the at least one LET joint to form a hinge to angularlydeflect, repeatedly, the two regions of rigidity from a planarconfiguration of the single-piece substrate to a non-planarconfiguration of the single-piece substrate, and from the non-planarconfiguration of the single-piece substrate to the planar configurationof the single-piece substrate.
 2. The method of claim 1, wherein thelocalized region of flexibility elastically accommodates substantiallyall stresses and strains in the single-piece substrate caused by angulardeflection of the two regions of rigidity.
 3. The method of claim 1,wherein the localized region of flexibility is a geometrically modifiedregion of the single-piece substrate.
 4. The method of claim 3, whereinthe plurality of compliant joints include at least one compliant jointformed by geometrical shaping of the single-piece substrate.
 5. Themethod of claim 4, wherein the at least one compliant joint formed bygeometrical shaping of the single-piece substrate is a LET joint.
 6. Themethod of claim 4, wherein the at least one compliant joint formed bygeometrical shaping of the single-piece substrate includes an array ofLET joints as least one of in series or in parallel.
 7. The method ofclaim 1, wherein the at least one LET joint includes two torsionalmembers and two bending members as sides of a rectangle circumscribing arectangular slot cut in the localized region of flexibility.
 8. Themethod of claim 7, wherein the at least one LET joint is configured totransfer a bending load associated with angular deflection of the tworegions of rigidity and applied to the at least one LET joint as atorsional load on the two torsional members of the at least one LETjoint.
 9. The method of claim 1, wherein the single-piece substrate is aconductor clad substrate.
 10. The method of claim 1, further comprising:disposing an electrically conducting trace running across the localizedregion of flexibility to provide an electrical connection to at leastone electronic component mounted on at least one of the two regions ofrigidity.
 11. The method of claim 1, wherein the single-piece substrate,includes a plurality of localized regions of flexibility disposed alongfold axes of an origami pattern.
 12. A method, comprising: forming alocalized region of flexibility separating two regions of rigidity in aprinted circuit board, the localized region of flexibility having alower rigidity than the two regions of rigidity, the localized region offlexibility separating the two regions of rigidity, the localized regionof flexibility including a plurality of compliant joints, the pluralityof compliant joints including at least one lamina emergent torsional(LET) joint; and configuring the plurality of compliant joints includingthe at least one LET joint to form a hinge to angularly deflect the tworegions of rigidity, repeatedly, from a planar configuration of theprinted circuit board to a non-planar configuration of the printedcircuit board, and from the non-planar configuration of the printedcircuit board to the planar configuration of the printed circuit board,at least one of the two regions of rigidity of the printed circuit boardis configured to receive an electronic device component mounted thereon.13. The method of claim 12, wherein the localized region of flexibilityelastically accommodates substantially all stresses and strains in theprinted circuit board caused by angular deflection of the two regions ofrigidity.
 14. The method of claim 12, wherein the plurality of compliantjoints include at least one geometrically shaped compliant joint in theprinted circuit board.
 15. The method of claim 14, wherein the at leastone geometrically shaped compliant joint in the printed circuit boardincludes at least one LET joint.
 16. The method of claim 15, wherein theat least one LET joint includes: two torsional members and two bendingmembers as sides of a rectangle circumscribing a rectangular slot cut inthe localized region of flexibility, and wherein the at least one LETjoint transfers a bending load associated with angular deflection of thetwo regions of rigidity and applied to the LET joint as a torsional loadon the two torsional members of the at least one LET joint.
 17. Themethod of claim 12, further comprising: an electrically conducting tracerunning across the localized region of flexibility.
 18. The method ofclaim 12, wherein the localized region of flexibility includes aplurality of localized regions of flexibility along fold axes of anorigami pattern.
 19. A method, comprising: geometrically modifying asingle-piece substrate by disposing a plurality of compliant jointsincluding at least one lamina emergent torsional (LET) joint in alocalized region of flexibility separating two regions of rigidity, thelocalized region of flexibility having a lower rigidity than the tworegions of rigidity; and configuring the plurality of compliant jointsincluding the at least one LET joint as a hinge to angularly deflect thetwo regions of rigidity, repeatedly, by more than 90° from a planarconfiguration of the single-piece substrate to a non-planarconfiguration of the single-piece substrate.
 20. The method of claim 19,further comprising: configuring the localized region of flexibilityseparating the two regions of rigidity as a hinge to angularly deflectthe two regions of rigidity, repeatedly, by 180°.